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Proof step 30 from proof vols-is-max-is-max-vols (previous step)

# vols0[v] = # vols1[v], # apebs = # wlar1, # wlar0 = # wlar1, avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, wlar0[m0] = wl-entry(m3, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar1[m0] = wl-entry(m4, used), ⌜m5⌝ = vols1[v][m], m < # vols1[v], m0 < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset1, wlar1), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, m0), valid-eraseq(apebs, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-eraseq(apebs, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-strong(apebs, to-vtbl(vols1), q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-wl(apebs, wlar0), valid-wl(apebs, wlar1), v ∈ vols0, v ∈ vols1, ∀ v0, m6, n. vols1[v0][m6] = ⌜n⌝ ∧ v0 ∈ vols1 ∧ m6 < # vols1[v0] ↔ wlar1[n].status = used ∧ n < # wlar1 ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v0 ∧ apebs[n].vidhdr.leb = m6 ∧ n ≠ m0 ⊦ ⌜m5⌝ = vols0[v][m], VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1

User applied rule all left

And obtained the following new goals

Proof step 31:
# wlar0 = # wlar1, # apebs = # wlar1, # vols0[v] = # vols1[v], avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, vols1[v][m] = ⌜m5⌝ ∧ v ∈ vols1 ∧ m < # vols1[v] ↔ wlar1[m5].status = used ∧ m5 < # wlar1 ∧ apebs[m5].vidhdr.valid? ∧ apebs[m5].vidhdr.vol = v ∧ apebs[m5].vidhdr.leb = m ∧ m5 ≠ m0, wlar1[m0] = wl-entry(m4, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar0[m0] = wl-entry(m3, used), ⌜m5⌝ = vols1[v][m], m0 < # wlar1, m < # vols1[v], bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, m0), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs, q1), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs, q0), valid-eraseq-strong(apebs, to-vtbl(vols1), q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-wl(apebs, wlar1), valid-wl(apebs, wlar0), v ∈ vols1, v ∈ vols0 ⊦ ⌜m5⌝ = vols0[v][m], VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0

Rule argument

pos: left 30 terms: v, m, m5 abort: F discard: T computed: T

Additional information

Used terms: v, m, m5